TY - JOUR
T1 - Non-unique results of collisions of quasi-one-dimensional dissipative solitons
AU - Descalzi, Orazio
AU - Brand, Helmut R.
N1 - Publisher Copyright:
© 2015 The Author(s) Published by the Royal Society. All rights reserved.
PY - 2015/12/13
Y1 - 2015/12/13
N2 - We investigate collisions of quasi-one-dimensional dissipative solitons (DSs) for a large class of initial conditions, which are not temporally asymptotic quasi-one-dimensional DSs. For the case of sufficiently small approach velocity and sufficiently large values of the dissipative cross-coupling between the counterpropagating DSs, we find non-unique results for the outcome of collisions. We demonstrate that these non-unique results are intrinsically related to a modulation instability along the crest of the quasione- dimensional objects. As a model, we use coupled cubic quintic complex Ginzburg Landau equations. Among the final results found are stationary and oscillatory compound states as well as more complex assemblies consisting of quasi-one-dimensional and localized states. We analyse to what extent the final results can be described by the solutions of one cubic quintic complex Ginzburg Landau equation with effective parameters.
AB - We investigate collisions of quasi-one-dimensional dissipative solitons (DSs) for a large class of initial conditions, which are not temporally asymptotic quasi-one-dimensional DSs. For the case of sufficiently small approach velocity and sufficiently large values of the dissipative cross-coupling between the counterpropagating DSs, we find non-unique results for the outcome of collisions. We demonstrate that these non-unique results are intrinsically related to a modulation instability along the crest of the quasione- dimensional objects. As a model, we use coupled cubic quintic complex Ginzburg Landau equations. Among the final results found are stationary and oscillatory compound states as well as more complex assemblies consisting of quasi-one-dimensional and localized states. We analyse to what extent the final results can be described by the solutions of one cubic quintic complex Ginzburg Landau equation with effective parameters.
KW - Complex Ginzburg Landau equation
KW - Dissipative solitons
KW - Localized structures
UR - http://www.scopus.com/inward/record.url?scp=84946021707&partnerID=8YFLogxK
U2 - 10.1098/rsta.2015.0115
DO - 10.1098/rsta.2015.0115
M3 - Article
AN - SCOPUS:84946021707
SN - 1364-503X
VL - 373
JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2056
M1 - 20150115
ER -